Acceptance for beneficial use document

Adding the Standard Hydrogen Monitoring Systems, VTP-PNL- 105K and VTP-PNL-205K to the Acceptance for Beneficial Use document, WHC-SD-WM-ABU-002

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic

New Developments in Quantum Algorithms

In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model. The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in time O(\log^c N). It outputs a quantum state describing the solution of the system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201

Cosmic Microwave Background Anisotropy with Cosine-Type Quintessence

We study the Cosmic Microwave Background (CMB) anisotropies produced by cosine-type quintessence models. In our analysis, effects of the adiabatic and isocurvature fluctuations are both taken into account. For purely adiabatic fluctuations with scale invariant spectrum, we obtain a stringent constraint on the model parameters using the CMB data from COBE, BOOMERanG and MAXIMA. Furthermore, it is shown that isocurvature fluctuations have significant effects on the CMB angular power spectrum at low multipoles in some parameter space, which may be detectable in future satellite experiments. Such a signal may be used to test the cosine-type quintessence models.Comment: 21 pages, 9 figure

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

From the Big Bang Theory to the Theory of a Stationary Universe

We consider chaotic inflation in the theories with the effective potentials phi^n and e^{\alpha\phi}. In such theories inflationary domains containing sufficiently large and homogeneous scalar field \phi permanently produce new inflationary domains of a similar type. We show that under certain conditions this process of the self-reproduction of the Universe can be described by a stationary distribution of probability, which means that the fraction of the physical volume of the Universe in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time, both at the stage of inflation and after it. This represents a strong deviation of inflationary cosmology from the standard Big Bang paradigm. We compare our approach with other approaches to quantum cosmology, and illustrate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.Comment: No changes to the file, but original figures are included. They substantially help to understand this paper, as well as eternal inflation in general, and what is now called the "multiverse" and the "string theory landscape." High quality figures can be found at http://www.stanford.edu/~alinde/LLMbigfigs

Hypersurface-Invariant Approach to Cosmological Perturbations

Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter (either a scalar or dust field) is solved by making an Ansatz which includes all terms quadratic in the spatial curvature. Gravitational radiation and scalar perturbations are treated on an equal footing. Our technique encompasses linear perturbation theory and it also describes some mild nonlinear effects. As a concrete example of the method, we compute the galaxy-galaxy correlation function as well as large-angle microwave background fluctuations for power-law inflation, and we compare with recent observations.Comment: 51 pages, Latex 2.09 ALBERTA THY/20-94, DAMTP R94/25 To appear in Phys. Rev.

Classical inflaton field induced creation of superheavy dark matter

We calculate analytically and numerically the production of superheavy dark matter (X) when it is coupled to the inflaton field \phi within the context of a slow-roll m_\phi^2 \phi^2/2 inflationary model with coupling g^2 X^2 \phi^2/2. We find that X particles with a mass as large as 1000 H_i, where H_i is the value of the Hubble expansion rate at the end of inflation, can be produced in sufficient abundance to be cosmologically significant today. This means that superheavy dark matter may have a mass of up to 10^{-3} Planck mass. We also derive a simple formula that can be used to estimate particle production as a result of a quantum field's interaction with a general class of homogeneous classical fields. Finally, we note that the combined effect of the inflaton field and the gravitational field on the X field causes the production to be a nonmonotonic function of g^2.Comment: 42 page LaTeX file with 8 PostScript figures included with eps